Number of states in taxi environment (Dietterich 2000)
This is more of a combinatorics than AI question but regradless, the full state information for the environment is:  

$(taxi \space position, passenger \space position, destination \space position)$

There are 25 possible taxi positions, 5 passenger positions and 4 destination positions making it $25 \cdot 5 \cdot 4 = 500$, so the paper is correct.  

You are also correct but you divided 1 objective into 2 objectives and you have 2 separate policies, a pickup policy and a dropoff policy. So your state information would be for each policy:

$(taxi \space position, destination \space position)$  

There are 25 possible taxi positions and 4 possible destination positions making it $25 \cdot 4 = 100$. You have 2 policies so you have $200$ states.

EDIT

Actually in the second case, I think you could get away with only 1 policy where you would simply change the destination position once you pick up the passenger so you dont need 2 separate policies and you would have only $100$ states